Solve for $x$ : $2x^2 + 8x - 24 = 0$
Dividing both sides by $2$ gives: $ x^2 + {4}x {-12} = 0 $ The coefficient on the $x$ term is $4$ and the constant term is $-12$ , so we need to find two numbers that add up to $4$ and multiply to $-12$ The two numbers $-2$ and $6$ satisfy both conditions: $ {-2} + {6} = {4} $ $ {-2} \times {6} = {-12} $ $(x {-2}) (x + {6}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -2) (x + 6) = 0$ $x - 2 = 0$ or $x + 6 = 0$ Thus, $x = 2$ and $x = -6$ are the solutions.